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Stochastic Sensitivity Analysis of Circadian Gene NetworkProject Staff
Project FundingStochastic effects have been shown
to play an important role in cellular processes from gene regulation to signal
transduction to metabolic pathways. These effects – coined as molecular
noise – give rise to a probabilistic description of the system dynamics
(chemical master equation), where reactions occur as discrete random events
(Markov process). As existing analysis tools based on a deterministic
approach are inadequate or inapplicable, this motivates the development of
formal analysis for stochastic systems. Here we propose a sensitivity
analysis methodology based on the Fisher information matrix, which is applied
to a Circadian gene network. The Fisher information matrix (FIM) describes
the (maximum) information that can be extracted from (random) measurements to
estimate model parameter values. Formally, this matrix is given by FIM = E["pf(y|p) "pf(y|p)T] where
f(y|p) is the conditional probability of measurements y
given parameters p, and E is the expected value operator. The FIM can be
interpreted as a consolidation of sensitivities, which gives the basis of the
proposed sensitivity measures. In particular, we propose three FIM-based
sensitivity measures using the FIM eigenvalues and diagonals, and parameter
variances. The proposed methodology finds an application
in the analysis of the Circadian rhythm gene network of Drosophila
melanogaster. The stochastic system is simulated using Gillespie’s
stochastic simulation algorithm. The analysis suggests that there exists no
unique sensitivity value. Rather,
the molecular noise gives rise to distribution-based sensitivity
measures. The proposed analysis may
elucidate the role of molecular noise in cellular processes, which will lead
to improved drug design and delivery. Iterative Approach for Model Development in Systems BiologyProject Staff
Project FundingAn iterative scheme is introduced for model identification using available system knowledge and limited experimental measurements. Initially, measurements are selected to ensure a significant fraction of the model parameters are identifiable and to maximize the accuracy of the identifiable parameters. The optimal set of measurements are determined a priori using a geometric approach based on decomposition of the Fisher Information Matrix (FIM) into contributions from each measurement. The parameter estimation in the iterative scheme is decoupled into two parts. In the first step, the known network topology along with the partial measurements (optimal) is used in the State Regulator Problem (SRP) to obtain estimates of all unmeasured concentrations and reaction rates. The SRP approach is based on a premise that cellular processes have evolved regulatory structures that optimize the use of cellular resources preventing wasteful accumulation of intermediates and minimize the reaction fluxes. Here, the kinetics of the reaction rates are not used in obtaining the estimates. The full estimates of the concentrations and the reaction rates are used for estimating the parameters in the kinetic models using a Bayesian approach. In this approach the parameters involved in the kinetic form of each reaction are independently determined as opposed to simultaneously estimating parameters of the entire system from limited measurements. The newly obtained parameters are then tested for model validity/invalidity according to several criteria. If further model refinement is necessary as indicated by the model (in)validation test, the next step in the iterative process is the design of the “optimal” experiment that would provide rich experimental data for improving the parameter estimates in the subsequent iteration. This is achieved using the D-optimality criterion to identify experimental conditions that would drive the system such that measurements with maximum information are obtained. The proposed iterative scheme is used to develop a model for the caspase function in apoptosis and it is demonstrated that the proposed iterative procedure can give accurate model and parameters with a few iterations. The iterative scheme is developed for a very general nonlinear state space form and has application to model a wide range of cellular processes from gene regulation networks, signal transduction to metabolic networks. |
